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How to use this site

This site is a repository for lottodesigns (covering designs v,k,t,m where t m), also called wheels or lotto systems.

We store designs up to 90 numbers, combinations size up to 10 numbers and match condition up to 20:


3 v 90 (total numbers in the disign)
2k 10 (numbers in each combination - row lenght, set size, block size)
2 ≤ t ≤ k ≤ v ≤ 10 (guarantee, if the condition is respected - matches, points)
2 ≤ t < m ≤ 20 (condition - numbers to guess of v for the guarantee to be maintained)


This archive is organized grouping designs by block size (k)

select first the size of the combinations you are looking for:


 (a list of designs of the selected block size will appear)  

Now you can open the table where is your system.


(if you are looking for 51,5,2,7 you'll find it in the table v,5,2,7

Finally, when opening a table you can see and download the lottodesign by clicking on the icon



Tables can have different informations for each row, depending of the availibility of the corresponding lotto design.

Infact you may have some other different scenarios:

1) The design is available but it's owned by an external site   (click the link to navigate the page of the site)



2) Some design is related to a corresponding design called inverse. In this case you'll see this information in the Author field


Improvements for a special family of covering designs, when t=m, are stored in LaJolla web site. Here you coul'd see a reference to this kind of designs but you'll need to navigare LaJolla's archives to download combinations (and in case calculate the inverse system)

a covering design of this kind is identified using 3 parameters (because if t=m then v,k,t,m is obviously v,k,t,t then you say just v,k,t)



3) In some case, when no information is available about the lotto design, you'll see an empty row like the following





Left mouse click on lens icon    open combinations for view in a web page


Right mouse click on lens icon    open contextual menu and you can DIRECTLY SAVE in a text file

using "Save as..." command

Save target as...



Command name in contextual menu can be different depending of the browser you are using:

CHROME (english)

EDGE (italian)

CHROME (italian)


Lower Bound (theoretical minimum possible)

In Jenuary 2018 an extra column on the very right side of tables has been added.

Lower Bound is the theoretical minimum number of blocks. There are different formulas for computing a lower bound; it is also possible to prove that the lower bound is higher than the stated lower bound for particular set of parameters, and therefore the Lower Bound stated here might not be achievable at all.

However, it is not possible to construct a design with a number of blocks smaller than any Lower Bound.

The Lower Bound number is important because it gives indication when it is appropriate to stop the search for improvements: definitely, when the Lower Bound is attained, and quite likely, when the known design has a number of blocks very close to it.

Calculating this number is not easy; a lot of theoretical knowledge needs to be applied. Usually, lower bounds are computed by several formulas, and the results are compared. The highest value is the value presented in this site, but we do not provide 100% guarantee that all the literature has been checked.

Another value similar to Lower Bound is called Volume Bound or just Theoretical Minimum, but it's not the same.

Volume Bound (Th.Min.) is calculated by dividing the total number of blocks available for use by the number of blocks covered by a single block.

Volume Bound is always less than or equal to Lower Bound; which means Lower Bound always gives the most meaningful value.


Volume Bound for 30,5,5,19 is 13 (Computed by rounding up the ratio C(30,5)/C(19,5)=142506/11628).

Lower Bound is 39

So we can definitely say there is no possible solution using less than 39 blocks (in spite of what the volume bound suggests); currently the world record uses 51 blocks.


As you can see in many tables, when Lower Bound value matches the number of Blocks B, The number corresponding to B is in bold:

(this mean the designs is perfect and it cannot be improved more)






The archive of designs is subjected to continues changes. Usually because authors improves and finds always better designs (in terms of less numbers of blocks used for the same guarantee).

That's why we have the Improvements page that contains a list of recents improvements (sorted by date or registration).

In the summary you'll see the v,k,t,m parameters, the new Author owner of the improvement, the old bound before the improvement and the date of publication.


The page lenght is fixed to 500 rows (for limiting the web page loading time).

However the full list of improvements is available. To see the all time improvements list you can download the text file by clicking on the link at the bottom of the same page.

Unfortunately that's not all...

For the reason that somethimes, over the normal activity of improvements and periodic updates, it is necessary to apply many adjustements to the archive at once (or simply because very large amounts of data can be refreshed in a single operation and it's not necessary to list so many changes between activities 'of routine'), you'll see another section in this site.

The Maintenance page is a registry of other improvements and changes (or corrections) that are not listed somewhere else but they could be needed to reconstruct the history of modifications.


Every maintenance session is listed on the page separately, but the text file containing the full list is available for download at the end of the page.


Then, in case you need to reconstruct the full history of a lottodeigns you should need to merge the two downloaded files ("ChronoImprovements.csv" from Improvements page and "ChronoMaintenance (date sorted).csv" from Maintenance page)

For merging the two files together into a single file you can use a simple text editor.

Later you'll need to sort the complete file by parameters (v,k,t,m column) using a datasheet.

Finally you'll see infomations of each designs grouped together:

In this way, if you search for a designs 'till its parameters you'll find one or more consecutives entryes regarding all improvements of it (in the example above look for the 90,8,5,9 design; All changes are grouped by rows).


The history reconstruction operation should be implemented as an internal function of the site, but for the while you'll need to operate manually.




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